[EM] election's utility approach

[Richard Moore]

MIKE OSSIPOFF wrote:
> But is there a demonstration that the voter's expectation is
> maximized by voting for all the candidates who are better than
> the voter's expectation in the election?

No, in fact I already showed a counter-example.

> As for the delta-p method, the delta-p are less fundamental, and
> farther from what's estimatable, as compared to the Pij, or especially the
> Wi. Estimating the Wi is at least not out of the question. Directly
> estimating the delta-p is out of the question. Richard would have to
> show a way to calculate estimates of the delta-p, one that makes good
> on that freedom from approximation that he spoke of. That method would
> have to not use approximations like the assumption that ties will
> be 2-way, and would have to not use the Pij to calculate the delta-p.

delta-p are actually more fundamental, though maybe harder to determine.
Any increase in probability of a win for a candidate with utility U
represents an increase in the expected utility equal to the product
of delta-p and U. It falls out of differentiating the expected utility
with respect to votes for a particular candidate.

In terms of accuracy, I would rank the four methods I listed as
method 1 > method 2 > (method 3 ~= method 4). I don't know which of
the last two is better.

In terms of ease of use, I would rank them as method 4 > method 3 >
method 2 > method 1. But the gap between methods 3 and 2 is much
greater than the other gaps.

> Richard, what's a precise way to calculate an estimate of the delta-p?

A challenging question, that. I'll look into it if I can.

> By the way, you left out Crannor's and Hoffman's ways of estimating
> the Pij, from the vote totals in a previous election. It seemed to
> me that Crannor's descripion of her method didn't give enough 
> information about it. If anyone understands Crannor's method, would
> they explain it? It sounds good, because it avoids the great
> amount of calculation work and complexity of Hoffman's method.

I don't know either of those methods. Could you fill me in?

  -- Richard